CC BY 4.0Karthik Ravichandran, ShreyasShreyasKarthik RavichandranBinh Huy NguyenSchneider, MattiMattiSchneider2025-11-052025-11-052025-10-06https://publica.fraunhofer.de/handle/publica/498144https://doi.org/10.24406/publica-603710.1007/s00466-025-02694-210.24406/publica-6037Two different sources of error emerge when computing the effective properties of materials with random microstructure: the random error which quantifies the fluctuations of the apparent properties computed on volume elements of finite size and the systematic error which is caused by the finite size of the considered volume element. Whereas the random error is apparent in computations, the systematic error is more subtle and requires much more effort to determine. How quickly these two errors decay for increasing volume-element size strongly depends on the way the volume element is selected - whereas the systematic error decays much faster than the random error for periodized ensembles, the opposite is true for snapshot ensembles in three spatial dimensions. Snapshot ensembles select the volume element as a part of a larger microstructure and correspond to the "real-world scenario" where a test specimen is cut from a larger material sample. Therefore, quantifying both the random and the systematic error for industrial composites is interesting and helpful for engineering applications. The work at hand studies the systematic and the random error for generated microstructures endowed with linear elastic constituents, both for periodized and non-periodized microstructures. We utilize computational micromechanics methods based on the fast Fourier transform (FFT) and evaluate the effective Young’s modulus for composites with a plastic matrix and spherical as well as cylindrical reinforcements at industrial volume fractions. Moreover, we study the influence of the volume fraction on both the random and systematic errors, which leads to an unbiased variance-reduction strategy.enStochastic homogenizationRandom errorSystematic errorRandom microstructure500 Naturwissenschaften und Mathematikjournal article